In short
The archipelago has nine inhabited islands, fifteen hundred kilometres from the mainland. São Miguel, the main one, holds the crater lakes of Sete Cidades and Furnas, where stew is still cooked in the geothermal ground.
The Azores are among the best places in the world for watching cetaceans: some twenty species pass offshore, and sperm whales are present all year.
What it really costs
Housing and food cost less than on mainland Portugal, but transport weighs: moving between islands means a flight or a seasonal ferry, and it adds up fast.
The thermal springs at Furnas and Ferraria mostly charge, but modestly. The trails, the viewpoints and the craters are free.
What nobody tells you
The weather changes several times a day and can cancel a boat trip or hide a crater completely. Allowing two windows for anything that matters is the local rule.
Whale watching is regulated and done with licensed operators. Trips leave early and are booked the day before according to the forecast, not weeks ahead.
One island is not another: São Miguel is green and populated, Pico is a volcano of two thousand three hundred and fifty metres, Flores is remote. Chaining three islands in a week means spending the week in airports.